شاہ ولی اللہ كا نظریہ اخلاق و معاشرت

His distinction was that he reflected over the Islamic system and applied it upon the modem age. He proved that the teachings of Islam cover not only faith, beliefs and rituals of worship but also rule all the aspects of social and moral values of a Muslim. He proved with profound arguments that these fundamental principles prevail and govern the Muslim society and its ethics. Shah Waliullah had a broad vision and a versatile approach towards the different aspects of political, moral and social behaviors. The most important thing about his contributions is that his views are widely accepted and welcomed by the scholars who came after him.

Performance of Time Series Models under Structural Discontinuities and Discordant Observations

Existence of outliers and structural breaks whose nature is mutually unknown, in time series data offer challenges to data analysts by causing problems in model identification, estimation and validation. Therefore, the detection of these outliers is an important area of interest in time series. We have investigated outlier detection in time series data using Chen and Liu (1993) and Kaiser and Maravall (2001) methods. We have focused on performance of these procedures in the presence of AO, IO, LS, TC and explored the impact of SLS for the case of SARIMA(p,d,q)(P,D,Q) for p, q=0,1,2; d=0,1; P,Q,D=0,1. The study adds to the literature by critically analyzing the performance of various test statistics for outlier detection under different scenarios using simulation strategy (MCMC) and by collecting empirical evidence from time series data for Pakistan. The evidence is collected by analyzing empirical level of significance, empirical critical values and empirical rejection frequency. We have also explored the confusion between LS, AO and IO, and between SLS and IO, the magnitude of TC that can be ignored and the appropriate critical value (c) for AO, IO, LS, TC and SLS for different sample sizes in various time series models. We also explore the swamping and masking effects of outliers by comparing the Chen and Liu (CL) method with Kaiser and Maravall (2001) procedure for multiple outliers. Our results indicate that the existence of various types of outliers in different time series models generate bias of different nature and is affected by the factors like size of outliers, sample size and cut-off points, and non-normality of the sampling distribution. The simulated empirical critical values are found higher than the theoretical cut-off points, with the empirical level of significance affected by sample size, outlier size and the model parameter coefficients. The empirical power of the test statistics is generally not satisfactory for small sample size, large cut-off points and xviiilarge model coefficient. The empirical analysis is carried out by running the outlier detection procedures on quarterly and monthly measured time series of Pakistan with five possible types of outliers i.e. AO, IO, LS, TC and SLS. The behavior observed for these variables supports our earlier findings. This study has shown that neglecting the SLS may lead to poor statistical analysis as other types of outliers may not fully grasp the impacts caused by SLS. Our simulation analysis does not support the argument of Kaiser and Maravall (2001) of replacing IO by SLS. Application of the method for detecting and removing outliers and structural breaks reduces the residual‟s excess kurtosis, skewness and JB test remarkably. A number of shocks in all series under observation are identified. Amongst which majority are supported by the graphical representation. Existing procedures of outlier detection may provide misspecified results leading to erroneous analysis. Therefore, these identified outliers require support from real world. Finding supportive evidence from real world is done by connecting the indicated discordant observations with historical evidences which may give better understanding. Several „no outlier‟ cases indicate the weakness of adopted procedures. It is concluded that all statistical analysis must include the exercise for outlier detection as it realizes the additional information contained by these aberrant observations, provide insight about policy implementation tools and enable better forecasts. The cut-off point may be set higher to reduce spurious detections. The test statistic for Transient Change should be revisited to have effective identification. Seasonal Level Shift may be included in the list of potential outliers.